24 cos 4x – 32 sin 4x а. (с, + 4x) сos 4x + (c, + 3х) sin 4x b. c,e2x + C2e 3x + 3 sin x C. none of these

Q: 1 + sin 4x cos 4x + C 8. 13.

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Q: 20 a Show that sin (A + B) + sin (A – B) = 2 sin A cos B. b Hence find: i 2 sin 3x cos 2x dx ii sin…

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Q: 5. (a) Expand (1+x) and hence find the value of (1.02) correct to 4 decimal place 1+sin 0 m-1 1-sin…

A: First expand 1+x4 then find the value of 1.044 Using the identity, a+b4=a4+4a3b+6a2b2+4ab3+b4…

Q: -1x 54cos If cos -1 00, prove that b. a x² 2xy ,2 = sin C. COS a+ ab %3D 2

A: Introduction :

Q: a. Z1 Z2 = r1 r2 [cos(0, + 02) + j sin(0, + 02)] %3D Z1 =" [cos(0, - 02) +j sin(01 – 02)] b. | | Z2…

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Q: 5. In AABC, m2B = 90°. sin A = 2x + 1.5 and cos C = 3x – 0.9. Find x.

A: Given: In Triangle ABC∠B=90οsinA=2x+1.5cosC=3x−0.9x=?

Q: Given that Y1 = x-1/2 cos x and y2 = x-1/2 sin x from a fundamental set of solutions of (--)- x²y" +…

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Q: 1. Determine solutions to sin 2x = , x€ [0, 2x) 2x sin() 2x 0.73 %3D %3D accurate to 2 decimal…

A: Explained below

Q: (1) Evaluate Hint: Express cos* x in terms of sin x. Then use the substitution u = sin a. Back…

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Q: cos(1) dt Using an appropriate substitution, evaluate: [2 + sin(1) ]* ™ 3 A +C [2+ sin(1) ]} B 3[2+…

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Q: Evaluating (A) (B S -3 of */2 si 57/2 18 18 ofth 0 (D) 9-x² dx using trigonometric substitution will…

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Q: Solve for x where x = [0,2π]. where x = [0,2]. State exact answers. Include sketches d cla m)…

A: SOLUTION-

Q: 2. : (a) For n ≥ 1, show that 1+z+2²+...+ 2¹: (b) Hence, show that 1+ cos 0 + cos 20 + 12+1 2 #1 7…

A: Solution:

Q: 3. Find g'(x) if g(x) = sin³(4x) %3D A. cos (4x) B. 3 sin?(4x) cos(4x) c. 12 sin (4x) cos(4x) D. 4…

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Q: 1 -p³e"l4 cos² e ,² dr sin0d0 ¢ do = x 32 πα X = ? 0 Jo

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Q: Q.3- Prove that: 2n 1 (cos =0 +i sin-) + 10 2cosne eino

A: The given problem is to prove the following complex identity. (cos n/5 θ +i sin 2n/10 θ)+1/einθ =…

Q: 4. (a) Express 3cos x-4 sin x in the form R cos(x+ a) where R>0 and 0 <a < (b) Hence find the…

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Q: The auxiliary roots of the auxiliary equation associated with a certain HLDE are m=±3, ±3i, + 3i.…

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Q: 1 1 1 cos a + cos 3a Cos a + cos 5a 1 Cos a + cos 7a +.... + cos a + cos(2n + 1)a 1 cosecaftan(n +…

A: Given that, We have to prove that, Consider the nth term of the left-hand side, By using the…

Q: /2 6 csc 0 a) [" r° cos 0 dr de 7/4

A: We can evaluate the given integral by using the following formula.

Q: 1. Convert the following expressions to its Julia equivalent. x+y² √√π-25) (a) e - cos' (2) sin³²…

A: We have to convert given expression to Julia equivalent. In Julia we have: a^b as ab exp(a) as ea…

Q: Q7: Í sin(3z)cos(4z) dz = a)cos z- cos(72) + C b) -tcus x -os(Ix) + C %3D Qe S sin'x cas d = 2).

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Q: (-1)"x2" Σ (2n)! 1. For all x E R, cos x = n=0 +00 (-16)"(4n+1) (2n)! c. Use the result in item 1(b)…

A: We have to prove the sum of series.

Q: 21. The general solution of 2 cos2 x – sin a -2 =0 is of the form x = An, b + 2nn, +2rn, n EI. The…

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Q: d) Find all solutions of cos 2x+2 sin² x – 2 sin x = 0. 5d. 6/7

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Q: a) Find all exact solutions on [0,2n) of 8sin?x + 6sinx + 1 = 0. b) Fine all exact solutions on [0,…

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Q: |(9 cos(9 x) +4 sin(4 x))dx =sin(9 x) - os Select one: True O False

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Q: 8. Solve: a sin() = { b 2 cos(a +) +1=0 on <a << 3 algebraically. on 0<a <10 using technology. %3D

A: 8.a) sinx5=23 on 0&lt;x&lt;10πb) 2cosx+π4+1=0 on π&lt;x&lt;3π

Q: Зл ,2n) then tg 2 1 If α te( V1- cos“(a – n) + a)+ = 0. 3n – 2a sin(5n + a) 1- sin 2

A: We have to prove the trigonometric equation.

Q: One of the correct steps to evaluate A B) None Ⓒ [+ + [ 1².40-16.4040] -S de cos 40d0 + [ 140 + 1 =…

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Q: Find the value of k if 1 х cos(3x) dx 1 3* x sin(3x) + — сos (3x) + C. k

A: .1. ʃ (u.v)dx= u ʃv.dx - ʃ(d/dx(u) . ʃv.dx)dx       Where u and v are function of x 2. ʃ sin(ax) dx=…

Q: . (a) Write cos 3x + i sin 3x = e3ix = (cos x + i sin x)³ by Euler's formula, expand, and equate…

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Q: 0.2 Use Euler's identity to (a) show that (i) cos(0 – 1/2) = sin(0), (ii) – sin(0 – 1/2) = cos(0),…

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Q: + i sin 12 22 = 2| cos 12 5m + i sin 12 5. Let z1 = 4 cos and 12 Find z,2, and

A: Given complex numbers are in polar form. For multiplication of polar numbers, the magnitudes are…

Q: r(cos0+isin 0) with 0 (exact) in (0°,360°): а. z = 12-12i Z, =-3-3i z, =-4V3+ 4i b. с. Z3 = %3D

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Q: 7.32. Prove that for 05sr, -( . ) cos 2 cos (a) a(e -a) = sin 3r sin ba (6) (r-) - 7.33. Use Problem…

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Q: 19. Given 0 <0 < 2T, solve 2 cos² 0 +3 sin 0 = 3. ○ 등, 똥 6 6 ○ , 풍,풍 ○ , 풍, 똥 5w 6 ○ 풍, 풍 11.

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Q: 0.3- Prove that: n 2n 1 (cos =0 +i sin8) + 10 2cosne - 5 eine

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Q: 1. Solve the linear equations below on the interval 0 < 0 < 2n. Show ALL your work!! 2 cos(2x) =-V3…

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Q: (5e" + 6x + 5 cos z)da

A: The solution is given below

Q: The auxiliary roots of the auxiliary equation associated with a certain HLDE are m=±3, ±3i, ±3i.…

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Q: 1/12 216 sin (6x) dx Evaluate 7/18 V1-2 cos (6x)

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Q: One of the correct steps to evaluate A sin²20d0 [² B cos 40d0 C) None Ⓒ//ww D do + sin²20d0 Ⓒ = [ √…

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Q: now that cos(ak – a/2) 2 sin(a/2) E sin(ak) : (1 %3D Taking the difference of cos(ak), A cos(ak) =…

A: We have to solve given problem:

Q: z"- 4z'+5z = x sin3x- cos3x %3D

A: We first find the complementary solution  of the given differential equation by finding the roots of…

Q: dy is If y = csc (x³) then d.x %3D -6x² cos² (æ³) A sin? (æ³) -6x2 cos (x) sin² (æ³) B -6x² cos²…

A: Given : function y = csc2(x3)   To find : Derivative of the given function dydx?

Q: 40 0<0<-, find the exact valı 41' If sin 0 = (a) sin (20) (b) cos (20) (c) sin 2 -

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Q: 12. Find all values of 0 in the interval [0, 2n) that satisfy the equation: cos 20 + cos 0 = 0

A: We need to find value of θ.